Andy Murray and Kim Sears have had a baby daughter, the first child for the British tennis player.

The couple, who married in April last year, had been apart for some of the final weeks of Sears’s pregnancy, with Murray reaching the final of the Australian Open, only to be beaten by Novak Djokovic.

“Andy and Kim had a daughter in the early hours of Sunday morning and the family are doing well,” a spokesman for the couple said.

At a press conference after the final on 31 January, Murray said he was keen to get home to Oxshott, in Surrey, for the birth. “I’m quite looking forward to getting home now,” he said, admitting he had sometimes found it hard to concentrate on his game, being so far away from Sears.

“Regardless of today’s result, it’s been hard. Had I lost in the third or fourth round, it still would have been difficult with everything that’s happened. She’s been amazing, handled everything unbelievably well. I have to thank her for allowing me to play and stay here with everything that was going on.”

Both the Scottish first minister, Nicola Sturgeon, and her Labour counterpart, Kezia Dugdale, have tweeted congratulations to Murray and Sears.